Platz means "place" in a very broad sense—it can be a location, a position (like in a hierarchy), a space occupied by or reserved for someone, or a (city) square. A Hirsch is a male deer, i.e., a stag. Platzhirsch in the original sense is a hunting or forestry term that refers to the dominant stag in an area who lays claim to the resident hinds when they are in heat and fights off all competitors. It's used figuratively to indicate the leader of a group who claims all the rights and privileges such a position entails. In English, we would say he is the "alpha dog."